论文标题
KDV Soliton气体的广义流体力学
Generalized hydrodynamics of the KdV soliton gas
论文作者
论文摘要
我们在经典可集成的分散流体动力学中建立了孤子气体理论与广义流体动力学（GHD）之间的明确对应关系，多体量子和经典集成系统的流体力学理论。这是通过构建Korteweg-De Vries（KDV）方程的孤子气体的GHD描述来完成的。我们进一步预测了自由能密度和通量的确切形式，以及用于孤子气体的保守电荷和电流的静态相关矩阵的确切形式。为此，我们通过经典颗粒确定孤子的统计数据，并通过孤子气的数值模拟确认所得的GHD静态相关矩阵。最后，我们通过简单地借用GHD结果来表达孤子气体的猜想动力相关函数。原则上，其他猜想也可以立即获得，例如孤子运输波动的扩散和大探空功能。
We establish the explicit correspondence between the theory of soliton gases in classical integrable dispersive hydrodynamics, and generalized hydrodynamics (GHD), the hydrodynamic theory for many-body quantum and classical integrable systems. This is done by constructing the GHD description of the soliton gas for the Korteweg-de Vries (KdV) equation. We further predict the exact form of the free energy density and flux, and of the static correlation matrices of conserved charges and currents, for the soliton gas. For this purpose, we identify the solitons' statistics with that of classical particles, and confirm the resulting GHD static correlation matrices by numerical simulations of the soliton gas. Finally, we express conjectured dynamical correlation functions for the soliton gas by simply borrowing the GHD results. In principle, other conjectures are also immediately available, such as diffusion and large-deviation functions for fluctuations of soliton transport.
